Mixtures of Contaminated Shifted Asymmetric Laplace Factor Analyzers

聚类分析可以被定义为在数据中搜索感兴趣的组。当有限混合模型用于聚类分析时，称为基于模型的聚类。通常，新的基于模型的聚类方法的发展集中在高斯混合模型上。不幸的是，假设观测数据的子总体是高斯分布的往往是不现实的。本文提出的研究将通过开发非高斯分布的有限混合来扩展当前关于基于模型的聚类的文献。具体地说，将开发一种受污染的移位不对称拉普拉斯因子分析仪(MCSALFA)的混合物。该模型将非常适合于分析包含虚假、离奇或噪声观测的高维和大数据。特别令人感兴趣的是变量数量超过观察数量的数据集，例如来自微阵列基因表达分析的数据集。 从方法论角度看，MCSALFA将把因子分析模型和污染混合模型统一起来。它将利用一种稳健的参数估计方案，即一种对异常点不敏感的方案，该方案基于期望最大化(EM)算法的变体。众所周知，使用EM算法来估计有限混合模型的参数可能是有害的，因为似然曲面通常包含许多局部极大值。因此，拟议研究的一个分支将通过不同的初始化战略来解决这一问题。一旦实施，申请者将出版一份手稿，记录该模型的推导和分类性能。此外，还将向世界各地的研究人员发布开源软件。 由基因表达微阵列分析产生的上述数据的例子只是许多可能的应用之一。充斥着虚假观察的数据，如来自社会经济研究和感官研究的数据，也将成为目标。申请者将建立一个专注于开发非高斯混合模型的研究计划。拟议的研究项目将通过为本科生和研究生提供合适的项目，为该研究项目提供坚实的基础。此外，由于拟议研究的应用范围将是深远的，学生将有机会与其他领域的研究人员合作。

Cluster analysis can be defined as the search for interesting groups within data. When a finite mixture model is used for cluster analysis, it is called model-based clustering. Typically, the development of novel model-based clustering approaches has focused on the Gaussian mixture model. Unfortunately, the assumption that the subpopulations of the observed data are Gaussian distributed is ofttimes unrealistic. The research proposed herein will extend the current literature on model-based clustering via development of finite mixtures of non-Gaussian distributions. Specifically, a mixture of contaminated shifted asymmetric Laplace factor analyzers (MCSALFA) will be developed. This model will be well suited for the analysis of high-dimensional and big data that contain spurious, outlying, or noisy observations. Of special interest are data sets whose number of variables exceeds the number of observations, like those arising from microarray gene expression analysis. From a methodological standpoint, the MCSALFA will unify the factor analysis model and the contaminated mixture model. It will utilize a robust parameter estimation scheme, i.e., one that is not sensitive to outlying points, that is based on a variant of the expectation-maximization (EM) algorithm. It is well-known that using the EM algorithm to estimate the parameters of a finite mixture model can be detrimental because the likelihood surface typically contains many local maxima. As such, one offshoot of the proposed research will be addressing this concern via different initialization strategies. Once implemented, the applicant will publish a manuscript documenting the model's derivation and classification performance. In addition, open-source software will be released for researchers around the world. The aforementioned example of data arising from gene expression microarray analysis is only one of many possible applications. Data rife in spurious observations, like those arising from socio-economic studies and sensory studies, will also be targeted. The applicant will establish a research program that focuses on the development of non-Gaussian mixture models. The proposed research project will provide a strong foundation for this research program by providing suitable projects for both undergraduate and graduate students. In addition, because the applications of the proposed research will be far reaching, opportunities for students to collaborate with researchers from other fields will arise.